Finite Group Databasebeta

← Prev (#28385808) Next (#28385810) →

C5×C37×D13⋊C3 #28385809

order14430
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C37 · Schur multiplier (H2) = C1

Aliases

direct productC5×C37×D13⋊C3
unambiguous semidirect productD13⋊(C3×C5×C37)
unambiguous semidirect product(C13⋊C3)⋊(C2×C5×C37)
unambiguous semidirect product(C5×D13)⋊(C3×C37)

Splittings

Fitting, socle, HallC5×C13×C37 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C5×C37
HallC5×C37×C13⋊C3 ⋊ C2
HallC5×D13×C37 ⋊ C3
HallC37×C13⋊C3 ⋊ C2×C5
HallD13×C37 ⋊ C3×C5
HallC13×C37 ⋊ C2×C3×C5
HallC5×C13⋊C3 ⋊ C2×C37
HallC5×D13 ⋊ C3×C37
HallC5×C13 ⋊ C2×C3×C37
HallC13⋊C3 ⋊ C2×C5×C37
HallD13 ⋊ C3×C5×C37

Subgroups

subgroupG/H
center, hypercenterC5×C37D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C5×C37
FrattiniC1G
Fitting, socleC5×C13×C37C2×C3
LCSG ▷ C13
UCSC1 ◁ C5×C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2405

Conjugacy classes & character table

1480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C37×AGL(1,𝔽13), C5×#19153503, C5×D37×D13⋊C3, …
maximal normal subgroup ofC5×C37×AGL(1,𝔽13), C5×#19153503, C5×D37×D13⋊C3, …
maximal quotient ofC5×C37×Dic13⋊C3, C2×C5×C37×D13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14430, 26);